SSC Maths Chapterwise E-book - PDF

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EducatedArithmetic

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This PDF document is a chapter-wise e-book of mathematics questions, likely aimed at students preparing for the SSC (Staff Selection Commission) exams. The book covers key concepts and includes multiple questions on topics like algebra, geometry and percentage along with other mathematical topics. It seems designed to assist students to enhance their problem-solving skills in preparation for competitive examinations.

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INDEX S.NO. CHAPTER NAME NO. OF QUESTIONS PAGE NO. 1. PERCENTAGE 262 7 – 44 2. PROFIT AND LOSS 163 45 – 68 3. DISCOUNT 209 69 – 98 4. SIMPLE INTEREST...

INDEX S.NO. CHAPTER NAME NO. OF QUESTIONS PAGE NO. 1. PERCENTAGE 262 7 – 44 2. PROFIT AND LOSS 163 45 – 68 3. DISCOUNT 209 69 – 98 4. SIMPLE INTEREST 56 99 – 108 5. COMPOUND INTEREST 133 109 –128 6. RATIO & PROPORTION 160 129 – 149 7. PARTNERSHIP 27 150 – 155 8. AVERAGE 195 156 – 183 9. TIME AND WORK 164 184 – 210 10. PIPE AND CISTERN 28 211 – 216 11. TIME AND DISTANCE 177 217 – 244 12. BOAT AND STREAM 26 245 – 249 13. MIXTURE 32 250 – 255 14. NUMBER SYSTEM 178 256 – 274 15. LCM & HCF 22 275 – 278 16. SIMPLIFICATION 225 279 – 305 17. TRIGONOMETRY 286 306 – 342 18. HEIGHT AND DISTANCE 45 343 – 350 19. ALGEBRA 365 351 – 391 20. GEOMETRY 402 392 – 443 21. MENSURATION 2D 136 444 – 462 22. MENSURATION 3D 209 463 – 489 23. CO-ORDINATE GEOMETRY 06 490 – 491 24. DATA INTERPRETATION 572 492 – 671 Join Telegram- Maths by Aditya Ranjan PERCENTAGE 01 PERCENTAGE/(i zfr'krrk) SSC CGL 2021 (PRE) 4. The reduction of 15% in the price of salt enables a person to buy 2 kg more for 272. The reduced price 1. A sold a mobile phone to B at a gain of 25% of salt per kg (in Rs.) is: and B sold it to C at a loss of 10%. If C paid ued dh dher esa 15» dh deh] ,d O;fDr dks Rs.272 Rs. 5625 for it, how much did A pay (in Rs.) esa 2 fdXkzk vf/d ued [kjhnus esa l{ke cukrh gSA ued for the phone Rs.esa) dh ?kVh gqbZ dher izfr fdXkzk ( fdruh gS\ A us,d eksckby iQksu B dks25» ds ykHk ij cspk vksj SSC CGL 11.04.2022 (3rd Shift) B usbls C dks10» dh gkfu ij csp fn;kA ;fn C us (a) 20.40 (b) 22.16 r blds fy, #i;s 5625 dk Hkqxrku fd;k] rksA usiQksu ds (c) 24.25 (d) 25.00 fy, (#i;s esa) fdruk Hkqxrku fd;k Fkk\ si 5. In a manufacturing unit, it was noted that the SSC CGL 11.04.2022 (1st Shift) price of raw material has increased by 25% and an by (a) 5000 (b) 4800 the labour cost has gone up from 30% of the cost (c) 4500 (d) 5100 of raw material to 38% of the cost of the raw n 2. Some students (only boys and girls) from material. What percentage of the consumption different schools appeared for an Olympiad of row material be reduced to keep the cost the ja exam. 20% of the boys and 15% of the girls same as that before the increase? R s failed the exam. The number of boys who ,d fuekZ.k bdkbZ esa] ;g ns[kk Xk;k fd dPps eky dh passed the exam was 70 more than that of the dher esa 25» dh o`f¼ gqbZ gS vkSj Je ykXkr dPps eky a th girls who passed the exam. A total of 90 dh ykXkr ds 30» ls c 0 and x 4   2207 , what is the value 47. If 8x2 + 9x + 8 = 0, then the value of x3 + is: x4 x3  5 1  ;fn 8x2 + 9x + 8 = 0 g S] rks dk eku Kkr dhft,A  x  5 . of   x  SSC CHSL 01/06/2022 (Shift- 1) 1  5 1  ;fn x > 0 vkSj x 4   2207 g S] rks x  x 5  dk 999 199 x4   (a) (b) 212 212 eku D;k gksxk\ SSC CHSL 31/05/2022 (Shift- 2) 999 199 (c) (d) (a) 15127 (b) 15134 512 512 (c) 15141 (d) 15130 1  4 1  43. (2x + 3y + 4z) (4x2 + 9y2 + 16z2 – 6xy – 12yz – 48. If x –  x  4  ? = 11, what is the value of  8xz) = ? x  x  SSC CHSL 31/05/2022 (Shift- 2) 1  1  ;fn x – gS] rks x  x 4  dk eku D;k gksxk\ 4 (a) 8x3 + 27y3 + 64z3 + 72xyz = 11 r x   (b) 8x3 + 27y3 + 64z3 – 72xyz si (c) 8x3 + 27y3 – 64z3 + 72xyz SSC CHSL 01/06/2022 (Shift- 1) (d) 8x3 – 27y3 – 64z3 – 72xyz (a) 14159 (b) 14163 an by Simplify :/ljyhdj.k djs a% 44. (c) 15127 (d) 15131 2 49. Expand x + 2x + 3 about x = –2. n 3ab × (a + b)–1 × (a–1 + b–1) SSC CHSL 31/05/2022 (Shift- 3) x = –2 ds lanHkZxeas 2 + 2x + 3 dk izlkj djsaA ja SSC CHSL 01/06/2022 (Shift- 2) 1 R s 2 (a) (a  b) (b) 1 (a) (x – 2) – 2(x + 2) + 3 a th (b) (x + 2)2 – 2(x + 2) + 3 (c) (a + b) (d) 3 (c) (x + 2)2 + 2(x + 2) + 3 1 3x (d) (x – 2)2 – 2(x – 2) – 3 45. If x   5 , then the value of 2 will x 2x  2 – 5x ty a 1  be _________. 50. If x4 +   4  = 322, then what is the value of x3 x  di M 1 3x ;fn x  5 gS] rks 2 dk eku gksxkA 1  x 2x  2 – 5x  3  ? –  SSC CHSL 31/05/2022 (Shift- 3) x  5 2 1  1  (a) 2 (b) 5 ;fn x4 +  x 4  = 322 g S] rks 3  3  dk eku D;k gS\ –    x  3 5 SSC CHSL 01/06/2022 (Shift- 2) (c) (d) 5 3 (a) 16 (b) 76 (c) 96 (d) 46 4 1 46. If x   14159 , Then a Possible value of x4 a c A 51. If a + b = 2c, then the value of  is: a–c b–c 1 x is: x a c ;fn a + b = 2c g S] rks  dk eku D;k gksxk\ 1 1 a–c b–c ;fn x4   14159 g S] rksx  dk laHko eku D;k x4 x SSC CHSL 01/06/2022 (Shift- 2) gS\ 1 SSC CHSL 31/05/2022 (Shift- 3) (a) (b) 1 2 (a) 69 (b) 121 (c) 81 (d) 11 (c) 0 (d) –1 Aditya Ranjan (Excise Inspector) Selected gSSelection fnyk,axs 380 Join Telegram- Maths by Aditya Ranjan Algebra 52. If x + y + z = 25, x3 + y3 + z3 = 85 and xyz = 20, 57. Which among the below option can be a square then find the value of x2 + y2 + z2 – xy – yz – root of? zx. (x2 – 14x + 49) (x2 + 6x + 9) ;fn x + y + z = 25, x3 + y3 + z3 = 85 vkSjxyz = 20 fuEUfyf[kr dk oxZewy D;k gS\ ] rksx2 + y2 + z2 – xy – yz – zx dk eku Kkr djsaA gS (x2 – 14x + 49) (x2 + 6x + 9) SSC CHSL 01/06/2022 (Shift- 3) SSC CHSL 02/06/2022 (Shift- 2) (a) 2 (b) 1 (a) (x – 4) (x + 9) (b) (x – 1) (x + 17) (c) 4 (d) 3 (c) (x – 7) (x + 3) (d) (x – 3) (x + 8) 53. If x = 32, y = 33 and z = 35, then evaluate the 2 expression x3 + y3 + z3 – 3xyz. 3 = (x 2 + y 2), then the value of 58. If x  y3  3 ;fn x = 32, y = 33 vkSjz = 35 g S] rks O;atd 3 x +y + 3 z3 – 3xyz dk eku Kkr dhft,A x 2  y2 x  0, y  0 is: SSC CHSL 01/06/2022 (Shift- 3) xy (a) 1120 (b) 1000 r (c) 900 (d) 700 2 x 2  y2 ;f n  x 3  y 3  3 = (x2 + y2) r ks xy x  0, y  0 si  1  1  54. x   = 8.5, what is the value of  x 2  2  ? If  dk eku D;k gksxk% x x  an by   SSC CHSL 02/06/2022 (Shift- 2)  1  2 1  n ;fn x   = 8.5 g S] rks x  2  dk eku Kkr x x  2   (a) (b) x2 + y 3 dhft,A ja R s (c) 1 (d) x + y2 SSC CHSL 01/06/2022 (Shift- 3) 59. The factors of a2 – 1 – 2x – x2 are ____. a th (a) 70.25 (b) 74.25 (c) 72.25 (d) 75.25 a2 – 1 – 2x – x2 ds xq.ku[kaM gSaA 55. If 1.5x = 0.04y, then what will be the value of SSC CHSL 02/06/2022 (Shift- 3) ty a (a) (a – x – 1) (a – x – 1) y–x (b) (a + 1 + x) (a – 1 – x) yx ? di M (c) (a – x + 1) (a – x + 1) y–x (d) (a – x + 1) (a – x – 1) ;fn 1.5x = 0.04y g S] rksy  x dk eku D;k gksxk\ 1 7x SSC CHSL 02/06/2022 (Shift- 1) 60. If x   10 , then find the value of x x 2  1 – 8x 77 77. (a) (b) 73 72 1 7x ;f n x   10 gS] rks d k eku Kkr dhft,A 72 73 x x 2  1 – 8x (c) (d) 77 77 SSC CHSL 03/06/2022 (Shift- 1) (a) 3.5 (b) 4.5 A  1  1  56.  x –  = 7.5, what is the value of  x 2  2  ? If  (c) 2.5 (d) 5.5  x  x  61. If x – 2y = 3 and 2xy = 5, then find the value of  1  2 1  (x + 2y)2. ;fn  x –  = 7.5 g S] rks x  2  dk eku Kkr  x  x  ;fn x – 2y = 3 vkSj2xy = 5 g S] rks (x + 2y)2 dk eku dhft,A Kkr djsa SSC CHSL 02/06/2022 (Shift- 2) SSC CHSL 03/06/2022 (Shift- 1) (a) 54.25 (b) 58.25 (a) 29 (b) 27 (c) 60.25 (d) 56.25 (c) 30 (d) 28 Aditya Ranjan (Excise Inspector) Selected gSSelection fnyk,axs 381 Join Telegram- Maths by Aditya Ranjan Algebra 2 2 1 1 3  a – b +  b – c ³ +  c – a  ³ 62. If a  b   2  4, a  0, b  0, then the 67. The value of  - b²  ³ +  b² - c²  ³ +  c² - a²  ³ is 2 a b a² value of a4 + b4 is: equal to: 1 1 ;fn a  b   0, b  0 rks a4 + 2 2 3  2  4, a a – b + b – c ³ + c – a  ³  a² - b²  ³ +  b² - c²  ³ +  c² - a²  ³ dk eku ds cjkcj gksxk 2 a b b4 dk eku D;k gksxk% SSC CHSL 06/06/2022 (Shift 01) SSC CHSL 03/06/2022 (Shift- 1) (a) ab+bc+ca (b) 0 (a) 32 (b) 256 (c) 64 (d) 2 1 (c) 1 (d) 63. If a + b + c = 0, then find the value gee  a + b b +c c +a a 2  b2  c2 68. 16a² + 4b² + 9c² – 16ab + 12bc – 24ca = ?. a 2 – bc SSC CHSL 06/06/2022 (Shift 02) r (a) (4a – 2b + 3c)² a 2  b2  c2 ;fn a + b + c = 0 rks dk eku Kkr djsa\ si a 2 – bc (b) (4a – 2b – 3c)² (c) (4a + 2b – 3c)² an by SSC CHSL 03/06/2022 (Shift- 2) (d) (4a + 2b + 3c)² (a) – 1 (b) 1 n 69. If a + b = 8 and a – b = 6, then find the value of (c) 2 (d) – 2 ‘ab’. 64. If a – b = 3 and a3 – b3 = 999, then find the value ja ;fn a + b = 8 vkSja – b = 6 gks] rks ‘ab’ dk eku Kkr R s of a2 – b2. dhft,A ;fn a – b = 3 vkSja3 – b3 = 999 gS] rks of a2 – b2 dk a th SSC CHSL 06/06/2022 (Shift 02) eku Kkr dhft,A (a) 6 (b) 8 SSC CHSL 03/06/2022 (Shift- 2) (c) 5 (d) 7 ty a (a) 60 (b) 62 70. If p = 38, then the value of p(p2 + 3p + 3) is (c) 64 (d) 63 _________. di M 65. If X  1  2 1   X  5  ? ;fn p = 38 g S] rks p(p2 +3p + 3) dk eku Kkr dhft,A  – 3 2 , what is the value of x  x  SSC CHSL 06/06/2022 (Shift 03)  2 1  (a) 39313 (b) 59319 1 ;fn X  –3 2 gS] rks X  x 5  dk eku D;k (c) 39318 (d) 59318 x   gskxk\ 71. If a+b = 7 and a–b= 5 , then find the value of SSC CHSL 03/06/2022 (Shift- 3) 8ab (a²+b²)–(a–b)² (a) – 715 2 (b) – 717 2 ;fn a+b = 7 vkSja–b= 5 gS] rks 8ab (a²+b²)–(a– b)² dk eku Kkr dhft,A A (c) – 723 2 (d) – 720 2 SSC CHSL 07/06/2022 (Shift 01) 66. If (a–1)²+(b+2)²+(c–1)²=0, then the value of (a) 19 (b) 23 a²+b²+c² is: (c) 27 (d) 21 ;fn (a–1)²+(b+2)²+(c–1)²=0 g S] rks a²+b²+c² dk eku 72. If x+y=13, then (x-8)3+(y-5)3 is: D;k gksxk\ ;fn x+y=13 gS] rks(x-8)3+(y-5)3 dk eku gSA SSC CHSL 06/06/2022 (Shift 01) SSC CHSL 07/06/2022 (Shift 01) (a) 6 (b) 0 (a) 2197 (b) 0 (c) 2 (d) 1 (c) 169 (d) 13 Aditya Ranjan (Excise Inspector) Selected gSSelection fnyk,axs 382 Join Telegram- Maths by Aditya Ranjan Algebra 73. If x+y+z=0, then find the value of 1 78. If x –  11 and x > 0, what is the value of x² y² z² x + +. x² - yz y² - zx z² - xy  2 1   x – 2  ? x² y² z²  x  ;fn x+y+z=0 g ks] rksx² - yz + y² - zx + z² - xy dk 1  2 1  eku Kkr djsa ;fn x –  11 and x > 0 vkSjgS] rks  x – 2  x  dk x  SSC CHSL 07/06/2022 (Shift 03) (a) 2 (b) 1 eku D;k gksxk\ (c) 3 (d) 0 SSC CHSL 08/06/2022 (Shift- 2) (a) –11 123 (b) 55 5 1 1 r³ + 74. If r + = 11 , then the value of r is. (c) 11 123 (d) –55 5 r r² - r +1 3 2 79. If px + x + 3x + q is exactly divisible by (x + 2) and (x – 2), then the values of p and q r 1 1 r³ + are: ;fn r + = 11 g S] rks r dk eku Kkr dhft,A si r r² - r +1 ;fn px3 + x2 + 3x + q] (x + 2) vkSj(x – 2) ls iw.kZr% vkSjq ds eku gS% foHkkT; gS prks an by SSC CHSL 07/06/2022 (Shift 03) SSC CHSL 08/06/2022 (Shift- 3) 119 10 n (a) (b) 3 10 119 (a) p  – and q  4 4 ja 19 10 R s (c) (d) 3 10 109 (b) p  and q  4 4 a th 75. If x  10  11 , y  10 – 11 , then value of 7x2 – 50xy + 7y2 = ________. 3 (c) p  and q  – 4 4 ;fn x  10  11 , y  10 – 11 rks 7x2 – 50xy ty a + 7y2 dk eku Kkr dhft,A (d) p  – 3 and q  – 4 4 di M SSC CHSL 08/06/2022 (Shift- 1) (a) 344 (b) 704 80. If x3 + y3 = 416 and x + y = 8, then find x4 + y4. (c) 1360 (d) 386 ;fn x3 + y3 = 416 vkSjx + y = 8 g S] rks x4 + y4 dk eku 76. The expression x4 – 8x2 + m will be a perfect Kkr dhft,A square when the value of m is: SSC CHSL 08/06/2022 (Shift- 3) O;a td x4 – 8x2 + m ,d iw.kZ oxZ gksxkmtcdk eku (a) 3002 (b) 3204 gksxkA (c) 3004 (d) 3104 SSC CHSL 08/06/2022 (Shift- 1) (a) 2 (b) 16 x y 81. If 2z = x + y, then the value of x – z  y – z is: (c) 8 (d) 4 77. What is the value of the following expression? SSC CHSL 09/06/2022 (Shift- 1) A  x a  (a  b)  x b  (b  c)  x c  (a  c) (a) 0 (b) 1 22  b   32  c   6 –2  a  x  x  x  (c) 2 (d) 5 fuEufyf [kr O;atd dk eku D;k gksxk\ 82. If x – y = 25 and xy = 78, then what is the value of x2 + y??  x a  (a  b)  x b  (b  c)  x c  (a  c) ;fn x – y = 25 vkSjxy = 78 g S] rks x2 + y? dk eku D;k 22  b   32  c   6 –2  a  x  x  x  gksxk\ SSC CHSL 08/06/2022 (Shift- 2) SSC CHSL 09/06/2022 (Shift- 1) (a) 1 (b) 0 (a) 625 (b) 781 (c) 4 (d) 9 (c) 103 (d) 756 Aditya Ranjan (Excise Inspector) Selected gSSelection fnyk,axs 383 Join Telegram- Maths by Aditya Ranjan Algebra 83. If (ab + bc + ca) = 0, then what is the value of 88. If x + 2 y = 10 and 2xy = 9, then one of the value of x – 2y is:  1 1 1   2  2  2  ? ;fn x + 2 y = 10 vkSj2xy = 9 gS] rks x – 2y ds ekuksa  a – bc b – ca c – ab  eas ls ,d eku gSA ; fn (ab + bc + ca) = 0 gS] rks SSC CHSL 10/06/2022 (Shift- 2)  1 1 1  (a) 8 (b) 6  2  2  2  dk eku D;k gS\  a – bc b – ca c – ab  (c) 10 (d) 12 SSC CHSL 09/06/2022 (Shift- 1) 89. For what value(s) of k will the expression (a) 2 (b) 0 1 p p  k 2 be a perfect square ? (c) 1 (d) a + b + c 9 84. If (x + 2) and (x – 3) are the factors of 1 x² + k1x + k2 , then: K dsfdl eku@fdu ekuksa ds fy, O;atdp  p  k2 9 ;fn (x + 2) vkSj(x – 3), x² + k1x + k2 dsxq.kt gS] rks% ,d iw.kZ oxZ gksxk\ r SSC CHSL 09/06/2022 (Shift 02) SSC CHSL 10/06/2022 (Shift- 2) (a) k1 = 1 and k2 = – 6 si 1 1 (b) k1 = –1 and k2 = – 6 (a) k   (b) k   8 9 an by (c) k1 = –1 and k2 = 6 (d) k1 = 1 and k2 = 6 1 1 (c) k   (d) k   n 21 18 1  85. If k +    = 2, find the value of 8k × k × k. 90. What is the product of (x + a) and (x + b)? ja k  vkSj(x + b) dk xq.kuiQy D;k gS\ R s (x + a) 1  SSC CHSL 10/06/2022 (Shift- 3) ;fn k +   = 2 gS] rks 8k × k × k dk eku Kkr dhft,A a th k   2 (a) x + (a + b) x + ab SSC CHSL 09/06/2022 (Shift 02) (b) x2 + (a – b) x + ab (c) x2 + (a + b) x – ab ty a (a) 8 (b) 1 (c) 4 (d) 2 (d) x2 + (a – b) x – ab di M 91. If x + y + z = 10, x2 + y2 + z2 = 30, then the value (r – s)³ + (s – t)³ + (t – r)³ of x3 + y3 + z3 – 3xyz is __________. 86. Simplify 6(r – s)(s – t)(t – r) ;fn x + y + z = 10, x2 + y2 + z2 = 30 gS] rks x3 + y3 + z – 3xyz dk eku ---------------- gSA 3 (r – s)³ + (s – t)³ + (t – r)³ 6(r – s)(s – t)(t – r) dks ljy djsaA SSC CHSL 10/06/2022 (Shift- 3) (a) – 70 (b) – 10 SSC CHSL 09/06/2022 (Shift 02) (c) – 30 (d) – 50 1 1 (a) (b) SSC CGL MAINS 2021 6 2 2 1 1 A  1 (c) (d) 1. If  x   = 3, then what is the value of x6 + x– 3 4  x 87. If x 2 – 9x + 1 = 0, what is the value of 6 ? x8 – 6239x4 + 1? 2 ;fn x2 – 9x + 1 = 0 g S] rks x8 – 6239x4 + 1 dk eku ;fn  1 g S] rks x6 + x–6 dk eku D;k gS\ x   = 3 D;k gksxk\  x SSC CHSL 09/06/2022 (Shift- 3) SSC CGL MAINS (08/08/2022) (a) 1 (b) 0 (a) 6 (b) 2 (c) – 1 (d) 2 (c) –2 (d) –6 Aditya Ranjan (Excise Inspector) Selected gSSelection fnyk,axs 384 Join Telegram- Maths by Aditya Ranjan Algebra 2. If xy = – 6 and x³ + y³ = 19 (x and y are integers), 4. Factorize the given algebraic expression. 1 1 x³ + 27y³ + 64z³ – 36xyz then what is the value of –1  –1 ? fn, x, chtxf.krh; O;atd dk xq.ku[kaM dhft,A x ³ x y ;fn xy = – 6 rFkkx³ + y³ = 19 (x rFkky iw.kkZ ad gSa ) gks ] + 27y³ + 64z³ – 36xyz 1 1 SSC Phase X 02/08/2022 (Shift- 02) rksx –1  y –1 dk eku D;k gS\ (a) (x + 3y + 4z) (x² + 9y² + 16z² + 3xy + 12yz SSC CGL MAINS (08/08/2022) + 4xz) (a) –2 (b) 2 (b) (x + 3y + 4z) (x² + 9y² + 16z² – 12xy ² 3yz (c) –1 (d) 1 – 4xz) 3. If a + b = 6 and ab = 5, then what is the value of (c) (x – 3y – 4z) (x² + 9y² + 16z² – 3xy – 12yz a3 + b3? – 4xz) ;f n a + b = 6 rFkkab = 5 gS ] rksa3 + b3 dk eku D;k gS\ (d) (x + 3y + 4z) (x² + 9y² + 16z² – 3xy – 12yz – 4xz) SSC CGL MAINS (08/08/2022) 5. The algebraic expression 25x² + 16y² + 9z² – (a) 136 (b) 126 24yz – 30zx is equal to: r (c) 116 (d) 106 chth; O;atd 25x² + 16y² + 9z² – 40xy + 24 yz 4. If x + y = 1, then what is the value of x³ + 3xy + fuEufyf[kr eas ls fdlds cjkcj gS\ si – 30zx y3? SSC Phase X 02/08/2022 (Shift- 02) ;fn x + y = 1 gS ] rksx³ + 3xy + y3 dk eku D;k gksxk\ an by SSC CGL MAINS (08/08/2022) (a) (4y + 3z – 5x)² (b) (4y – 3z – 5x) (4x + 5y + 3z) n (a) 0 (b) 2 (c) (4y + 3z – 5x) (4x + 5y – 3z) (c) 1 (d) –1 (d) (4y – 3z – 5x)² ja R s SSC PHASE X (GRADUATE LEVEL) 2022 6. Find the value of a² + b² + c² – 2ab + 2ac – 2bc, if a = x + y, b = x – y and c = 2x – 1. a th a² + b² + c² – 2ab + 2ac – 2bc, dk eku Kkr dhft, 1 1 1 1. If 2x = 3y = 6z, then + – x y z is equal to: ;fn a = x + y, b = x – y vkSjc = 2x – 1 gS A SSC Phase X 04/08/2022 (Shift- 03) 1 1 1 ty a ;f n 2 = 3 = 6 g S rksx + y – z fuEu esa ls fdlds x y z (a) (x – y – 1)² (b) (2x + 2y – 1)² (c) 0 (d) (2x – 2y – 1)² cjkcj gS\ di M SSC Phase X 01/08/2022 (Shift- 03) 1  1 7. If x² + = 47,  x   is equal to: x²  x 3 (a) 1 (b) 2 1  1 ;f n x² + = 47  x   d k eku Kkr dhft,A –1 x²  x (c) 0 (d) 2 SSC Phase X 04/08/2022 (Shift- 03) 2. If (a + b) = 11 and (a – b) = 7, then find (a) 6, –6 (b) 9, –9 the value of a² b² (a² + b²). (c) 7, –7 (d) 8, –8 ;f n (a + b) = 11 v kSj(a – b) = 7 r ksa² b² 1 15 1 8. If x – = , find the value of x +. (a² + b²) d k eku D;k gksxk\ A x 4 x SSC Phase X 01/08/2022 (Shift- 03) 1 15 1 (a) 9 (b) 11 ;f n x – = g S] rks x+ e ku Kkr dhft, x 4 x (c) 7 (d) 5 SSC Phase X 04/08/2022 (Shift- 02) 3. If xy = 6 and x²y + xy² + x = y = 63, then the value of x² + y² is: 15 21 (a) (b) SSC Phase X 02/08/2022 (Shift- 02) 4 4 (a) 79 (b) 59 13 17 (c) (d) (c) 70 (d) 69 4 4 Aditya Ranjan (Excise Inspector) Selected gSSelection fnyk,axs 385 Join Telegram- Maths by Aditya Ranjan Algebra 9. What must be subtracted from x³ – 3x²y + 3xy² SSC CPO 2020 – y³ to get x³ – y³ ? x³ – y³ i zkIr djus ds fy, x³ – 3x²y + 3xy² – y³ 1. If a2 + b2 + c2 + 216 = 12 (a + b – 2c), then esa ls D;k ?kVk;k tkuk pkfg,\ ab – bc + ca is : SSC Phase X 04/08/2022 (Shift- 02) ;f n a² + b² + c² + 216 = 12(a + b – 2c) g S] rks (a) 3x²y – 3xy³ (b) x³ – y³ ab – bc  ca d k eku Kkr djsaA (c) –3x²y + 3xy² (d) –x³ + y³ SSC CPO 23/11/2020 (Shift-1) 10. If a – b = 10 and ab = 4, then the value of a³ (a) 6 (b) 4 – b³ + 4(a + b)² is: (c) 3 (d) 8 ;f n a – b = 10 v kSjab = 4 r ksa³ – b³ + 4(a + b)² d k eku gS% 2. If 5 5x 3 – 3 3y 3  ÷  5x – 3y  = SSC Phase X 04/08/2022 (Shift- 02) (a) 1280 (b) 1623  Ax 2 + By 2 + Cxy ,  the, the value of  3A + B –  r (c) 1584 (d) 1500 15C is: si 11. If P = x² – 100 and Q = x  10 , then the value ;f n (5 5x³ – 3 3y³)  ( 5x – 3y) = (Ax² + By² x² – 16 x–4 g S] rks (3A + B – 15C ) d k eku Kkr djsaA an by + Cxy) P SSC CPO 23/11/2020 (Shift-1) of is: n Q (a) 3 (b) 12 (c) 8 (d) 5 x² – 100 x  10 P ja P = v kSjQ = gS ] rks d k eku R s 4 –4 x² – 16 x–4 Q 3. If x + x = 194, x > 0, then the value of D;k gS\ a th 1 x+ is : SSC Phase X 05/08/2022 (Shift- 03) x x +10 x – 10 1 ;fn x4 + x–4 = 194, x > 0 g S] rksx  dk eku Kkr djsa ty a (a) (b) x +14 x+4 x SSC CPO 23/11/2020 (Shift-1) di M x – 10 x +10 (c) (d) (a) 4 (b) 14 x–4 x–4 (c) 6 (d) 8 1 6 1 4. If x 2 + 8y 2 – 12y – 4 xy + 9 = 0, then the value 12. If y + = 5, then the value of y  6 is: y y of (7x – 8y ) is: 1 1 ;f n x² + 8y² – 12y – 4xy + 9 = 0 g S] rks (7x – 8y) ;f n y + y = 5 g S] rksy6  6 d k eku D;k gS\ dk eku Kkr djasA y SSC CPO 23/11/2020 (Shift-2) SSC Phase X 05/08/2022 (Shift- 03) (a) 9 (b) 5 (a) 18 (b) 12 (c) 12 (d) 21 A (c) 10 (d) 15 5. If x 2 – 5x +1 = 0, then the value of 1 1  4 1  13. Find the value of x³ – when x – = 5.  x + 2  ÷  x +1 is : 2 x³ x  x   4  1 1 1 ;f n x² – 5x + 1 = 0 g S] rks x + x 2  ÷ (x² + 1) d k x³ – d k eku Kkr dhft,] tc x– =5 g ksA   x³ x eku Kkr djsaA SSC Phase X 05/08/2022 (Shift- 03) SSC CPO 23/11/2020 (Shift-2) (a) 150 (b) 125 (a) 21 (b) 25 (c) 140 (d) 100 (c) 24 (d) 22 Aditya Ranjan (Excise Inspector) Selected gSSelection fnyk,axs 386 Join Telegram- Maths by Aditya Ranjan Algebra 6. If x + y + z = 19, xyz = 216 and xy + yz + zx = 12. If a2 + b2 + c3 + 84 = 4 (a – 2b + 4c), then 114, then the value of x 3 + y3 + z3 + xyz is: ab – bc  ca is equal to: ; fn x + y + z = 19, xyz = 2016 vkSjxy + yz + zx ; fn a2 + b2 + c3 + 84 = 4 (a – 2b + 4c) gS] rks = 114 gS] rks x³ + y³ + z³ + xyz dk eku Kkr djsaA ab – bc  ca dk eku Kkr djsaA SSC CPO 23/11/2020 (Shift-2) SSC CPO 24/11/2020 (Shift-2) (a) 1441 (b) 361 (c) 1225 (d) 577 (a) 4 10 (b) 10 2 7. If x – 3x + 1 = 0, then the value of (c) 5 10 (d) 2 10  4 1  13. If x + y + z = 19, x + y + z2 = 133 and xz = y2, 2 2  x + 2  ÷  x +1 is: 2 x  x > z > 0, what is the value of (x – z)?  ; fn x + y + z = 19, x² + y² + z² = 133 vkSjxz =  4  1 y², x > z > 0 gS] rks(x – z) dk eku Kkr djsaA ; fn x² – 3x + 1 = 0 gS] rks x   ÷ (x² + 1) dk x²  SSC CPO 25/11/2020 (Shift-1)  (a) 0 (b) 5 eku Kkr djsaA (c) –2 (d) –5 r SSC CPO 24/11/2020 (Shift-1) (a) 5 (b) 6 14. If (5 5x³ – 3 3y³)  ( 5x – 3y) = (Ax² + By² + si (c) 7 (d) 9 Cxy), the what is the value of (3A – B – 15 C)? an by 8. If x + y + z = 17, xyz = 171 and xy + yz + zx = ; fn (5 5x³ – 3 3y³)  ( 5x – 3y) = (Ax² + By² +  x 3 + y3 + z 3 + xyz  is: n 111, then the value of 3 Cxy) gS] rks(3A – B – 15C) dk eku Kkr djsaA ; fn x + y + z = 17, xyz = 171 vkSjxy + yz + zx SSC CPO 25/11/2020 (Shift-1) ja R s = 111 gS] rks x  y  z  xyz dk eku Kkr djsaA 3 3 3 3 (a) 12 (b) 8 (c) –3 (d) –5 a th SSC CPO 24/11/2020 (Shift-1) 15. If x4 + x –4 = 194, x > 0, then what is the value (a) –64 (b) 0 1 (c) 4 (d) –4 of x + + 2? x If x2 + 8y2 + 12y – 4xy + 9 = 0, then the value ty a 9. of (7x + 8y) is: 1 ; fn x² + 8y² + 12y – 4xy + 9 = 0 gS] rks ; fn x4 + x–4 = 194, x > 0 gS] rksx + +2 dk eku di M (7x + 8y) x d k eku Kkr djsaA Kkr djsaA SSC CPO 24/11/2020 (Shift-1) SSC CPO 25/11/2020 (Shift-1) (a) –33 (b) 9 (a) 6 (b) 8 (c) 33 (d) –9 (c) 4 (d) 14 10. If x + y + z = 13, x2 + y2 + z2 = 133 and x3 + y3 16. If a²+ b² = 82 and ab = 9, then a possible value of a³ + b³ is: + z3 = 847, then the value of 2 xyz is: ; fn a² + b² = 82 vkSjab = 9 gS] rks a³ + b³ dk laHkOk ; fn x + y + z = 13, x² + y² + z² = 133 v kSjx³ + y³ eku Kkr djsaA + z³ = 847 gS] rks xyz dk eku Kkr djsaA 2 SSC CPO 25/11/2020 (Shift-2) SSC CPO 24/11/2020 (Shift-2) (a) 720 (b) 830 A (a) 8 (b) 7 (c) 750 (d) 730 (c) –9 (d) –6 17. If x + y + z = 19, xyz = 216 and xy + yz + zx = 11. If a3 + b3 = 217 and a + b = 7, then the value of 114, then the value of x³ + y³ + z³ + xyz is: ab is: ; fn x + y + z = 19, xyz = 216 vkSjxy + yz + zx ; fn a³ + b³ = 217 vkSja + b = 7 gS] rks ab dk eku Kkr djsaA = 114 gS] rks x³ + y³ + z³ + xyz dk eku Kkr djasA SSC CPO 24/11/2020 (Shift-2) SSC CPO 25/11/2020 (Shift-2) (a) –6 (b) –1 (a) 32 (b) 28 (c) 7 (d) 6 (c) 30 (d) 35 Aditya Ranjan (Excise Inspector) Selected gSSelection fnyk,axs 387 Join Telegram- Maths by Aditya Ranjan Algebra r si an by n ja R s a th ty a di M A Aditya Ranjan (Excise Inspector) Selected gSSelection fnyk,axs 388 Join Telegram- Maths by Aditya Ranjan Algebra ANSWER KEY SSC CGL Pre 2021 1. (b) 5. (d) 9. (a) 13. (b) 17. (b) 21. (c) 25. (b) 29. (a) 33. (a) 37. (d) 2. (a) 6. (b) 10. (d) 14. (a) 18. (d) 22. (b) 26. (a) 30. (b) 34. (c) 38. (a) 3. (c) 7. (c) 11. (a) 15. (a) 19. (c) 23. (a) 27. (d) 31. (a) 35. (a) 39. (d) 4. (b) 8. (a) 12. (a) 16. (d) 20. (a) 24. (d) 28. (a) 32. (d) 36. (d) 40. (b) SSC PHASE IX r si 1.(a) 2.(d) 3.(a) 4.(d) 5.(d) 6.(b) 7.(b) 8.(d) 9.(b) 10.(c) 11.(c) 12.(a) an by 13.(a) 14.(b) 15.(d) n ja R s SSC CGL Mains 2020 a th 1.(d) 2.(a) 3.(b) 4.(c) 5.(d) 6.(a) 7.(a) 8.(a) 9.(a) 10.(b) ty a 11.(b) 12.(a) di M SSC CGL Pre 2020 1.(c) 2.(d) 3.(b) 4.(c) 5.(b) 6.(a) 7.(a) 8.(d) 9.(c) 10.(a) 11.(c) 12.(c) 13.(a) 14.(d) 15.(b) 16.(b) 17.(a) 18.(b) 19.(b) 20.(d) 21.(a) 22.(d) 23.(d) 24.(a) 25.(a) 26.(c) 27.(c) 28.(c) 29.(b) 30.(c) A 31.(c) 32.(a) 33.(a) 34.(d) 35.(d) 36.(a) 37.(c) 38.(d) 39.(d) 40.(c) 41.(c) 42.(d) 43. (b) 44. (a) 45.(b) 46.(d) 47.(a) 48.(d) 49.(d) 50.(b) 51.(c) 52.(d) 53.(a) 54.(b) 55.(a) 56.(a) 57.(c) 58.(d) 59.(b) 60.(a) 61.(b) Aditya Ranjan (Excise Inspector) Selected gSSelection fnyk,axs 389 Join Telegram- Maths by Aditya Ranjan Algebra SSC CHSL 2020 1.(d) 2.(d) 3.(c) 4.(d) 5.(d) 6.(d) 7.(a) 8.(d) 9.(c) 10.(b) 11.(b) 12.(c) 13.(a) 14.(d) 15.(d) 16.(b) 17.(c) 18.(c) 19.(a) 20.(b) 21.(a) 22.(b) 23.(d) 24.(c) 25.(d) 26.(d) 27.(d) 28.(c) 29.(a) 30.(c) 31.(c) 32.(c) 33.(a) 34.(a) 35.(b) 36.(a) 37.(c) 38.(a) 39.(b) 40.(d) 41.(b) 42.(a) 43.(c) 44.(b) 45.(d) 46.(c) 47.(c) 48.(d) 49.(d) 50.(b) 51.(c) 52.(a) 53.(a) 54.(c) 55.(c) 56.(c) 57.(a) 58.(b) 59.(c) 60.(a) r 61.(b) 62.(c) 63.(d) 64.(d) 65.(a) 66.(b) 67.(d) 68.(b) 69.(c) 70.(a) si an by 71.(d) 72.(d) 73.(b) 74.(b) 75.(a) 76.(a) 77.(a) 78.(d) 79.(c) 80.(c) n 81.(b) 82.(c) 83.(a) 84.(a) 85.(a) 86.(b) 87.(a) 88.(b) 89.(c) 90.(d) ja R s 91.(b) 92.(d) 93.(c) 94.(d) 95.(b) 96.(c) 97.(a) 98.(d) 99.(d) 100.(b) a th 101.(d) 102.(b) 103.(c) 104.(d) 105.(a) 106.(a) 107.(c) 108.(c) 109.(c) 110.(a) ty a 111.(a) 112.(d) di M SSC CHSL 2021 1.(c) 2.(d) 3.(c) 4.(c) 5.(d) 6.(a) 7.(a) 8.(a) 9.(b) 10.(c) 11.(a) 12.(a) 13.(c) 14.(a) 15.(c) 16.(a) 17.(c) 18.(c) 19.(c) 20.(b) 21.(a) 22.(d) 23.(c) 24.(d) 25.(d) 26.(b) 27.(d) 28.(b) 29.(c) 30.(b) 31.(b) 32.(a) 33.(b) 34.(b) 35.(d) 36.(b) 37.(a) 38.(c) 39.(a) 40.(a) 41.(c) 42.(a) 43.(d) 44.(d) 45.(c) 46.(d) 47.(c) 48.(c) 49.(b) 50.(b) A 51.(b) 52.(d) 53.(d) 54.(a) 55.(d) 56.(b) 57.(c) 58.(a) 59.(b) 60.(a) 61.(a) 62.(d) 63.(c) 64.(b) 65.(b) 66.(a) 67.(d) 68.(b) 69.(d) 70.(d) 71.(a) 72.(b) 73.(a) 74.(a) 75.(a) 76.(c) 77.(a) 78.(b) 79.(d) 80.(d) 81.(c) 82.(b) 83.(b) 84.(b) 85.(a) 86.(b) 87.(b) 88.(a) 89.(d) 90.(a) 91.(b) Aditya Ranjan (Excise Inspector) Selected gSSelection fnyk,axs 390 Join Telegram- Maths by Aditya Ranjan Algebra SSC CGL Mains 2021 1.(c) 2.(d) 3.(b) 4.(c) SSC PHASE X (GRADUATE LEVEL) 2022 1.(c) 2.(a) 3.(d) 4.(d) 5.(a) 6.(b) 7.(c) 8.(d) 9.(c) 10.(c) 11.(b) 12.(a) 13.(c) SSC CPO 2020 r 1.(a) 2.(a) 3.(a) 4.(a) 5.(d) 6.(c) 7.(b) 8.(d) 9.(a) 10.(d) si 11.(d) 12.(d) 13.(b) 14.(c) 15.(a) 16.(d) 17.(d) an by n ja R s a th ty a di M A Aditya Ranjan (Excise Inspector) Selected gSSelection fnyk,axs 391 Join Telegram- Maths by Aditya Ranjan Geometry 20 GEOMETRY/(T;kfefr) SSC CGL Pre 2021 ,d leckgq f=kHkqt ABC dsanz O okys o`Ùk esa mRdhf.kZr gSA y?kq pkiBC ij ,d fcanq D gSvkSjCBD = 40° gS A 1. AB is a diameter of a circle with centre O. A tangent is drawn at point A. C is a point BCD dk eki Kkr dhft,A on the circle such that BC produced meets the tangent at P. If APC = 62°, then find the SSC CGL 11.04.2022 (1st Shift) measure of the minor arc AC. (a) 30° (b) 50° AB dsanzO okys o`Ùk dk O;kl gSAAfcanq ij Li'kZ js[kk [khaph (c) 20° (d) 40° tkrh gSA C o`Ùk ij ,d ,slk fcanq gS ftlls BC dks vkxs c